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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 471 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 85 (b) 168 (c) 84 (d) 15
  2. 2.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 39 (b) 230 (c) 420 (d) 210
  3. 3.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 12 (b) 14 (c) 10 (d) 11
  4. 4.Which term of the AP 17, 21, 25, 29, … is 93? (a) 21st (b) 22nd (c) 20th (d) 19th
  5. 5.What is the missing term in the AP 8, 11, 14, ?, 20? (a) 17 (b) 20 (c) 18 (d) 16
  6. 6.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 222 (b) 31 (c) 111 (d) 126
  7. 7.What is the 12th term of the AP 11, 13, 15, 17, …? (a) 33 (b) 24 (c) 22 (d) 35
  8. 8.What is the sum of all the whole numbers from 1 to 60? (a) 1800 (b) 3660 (c) 1770 (d) 1830
  9. 9.What is the missing term in the AP 5, ?, 17, 23, 29? (a) 12 (b) 10 (c) 11 (d) 17
  10. 10.What is the missing term in the AP 13, 17, 21, ?, 29? (a) 24 (b) 25 (c) 26 (d) 29
  11. 11.What is the 40th term of the AP 12, 17, 22, 27, …? (a) 207 (b) 195 (c) 212 (d) 200
  12. 12.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 32 (b) 183 (c) 360 (d) 180
  13. 13.What is the 11th term of the AP 16, 25, 34, 43, …? (a) 99 (b) 115 (c) 106 (d) 90
  14. 14.What is the 10th term of the AP 6, 14, 22, 30, …? (a) 80 (b) 78 (c) 86 (d) 72
  15. 15.Which term of the AP 6, 13, 20, 27, … is 216? (a) 32nd (b) 30th (c) 31st (d) 33rd
  16. 16.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 729 (c) 53 (d) 378
  17. 17.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 252 (b) 504 (c) 32 (d) 264
  18. 18.What is the 33rd term of the AP 19, 27, 35, 43, …? (a) 283 (b) 264 (c) 275 (d) 256
  19. 19.What is the 34th term of the AP 5, 10, 15, 20, …? (a) 165 (b) 170 (c) 175 (d) 171
  20. 20.What is the sum of all the whole numbers from 1 to 48? (a) 1152 (b) 1176 (c) 2352 (d) 1128
  21. 21.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 272 (d) 31
  22. 22.What is the 32nd term of the AP 6, 14, 22, 30, …? (a) 262 (b) 248 (c) 256 (d) 254
  23. 23.Which term of the AP 1, 4, 7, 10, … is 97? (a) 33rd (b) 35th (c) 34th (d) 32nd
  24. 24.What is the missing term in the AP 1, ?, 11, 16, 21? (a) 7 (b) 6 (c) 5 (d) 11
  25. 25.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 672 (b) 50 (c) 360 (d) 336
  26. 26.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 28 (b) 95 (c) 180 (d) 90
  27. 27.What is the sum of all the whole numbers from 1 to 23? (a) 277 (b) 276 (c) 253 (d) 552
  28. 28.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 8 (b) 36 (c) 35 (d) 70
  29. 29.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 352 (b) 187 (c) 176 (d) 26
  30. 30.Which term of the AP 20, 28, 36, 44, … is 284? (a) 34th (b) 35th (c) 36th (d) 33rd
  31. 31.What is the 16th term of the AP 5, 10, 15, 20, …? (a) 85 (b) 75 (c) 80 (d) 81
  32. 32.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 429 (b) 396 (c) 66 (d) 792
  33. 33.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 804 (b) 432 (c) 402 (d) 61
  34. 34.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 39 (d) 400
  35. 35.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 384 (b) 57 (c) 708 (d) 354
  36. 36.What is the sum of all the whole numbers from 1 to 85? (a) 3655 (b) 3656 (c) 3570 (d) 7310
  37. 37.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 3003 (c) 6162 (d) 3081
  38. 38.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 232 (c) 462 (d) 210
  39. 39.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 41 (b) 312 (c) 588 (d) 294
  40. 40.What is the sum of all the whole numbers from 1 to 93? (a) 8742 (b) 4371 (c) 4278 (d) 4372

Answer key

  1. 84
  2. 210
  3. 11
  4. 20th
  5. 17
  6. 111
  7. 33
  8. 1830
  9. 11
  10. 25
  11. 207
  12. 180
  13. 106
  14. 78
  15. 31st
  16. 729
  17. 252
  18. 275
  19. 170
  20. 1176
  21. 256
  22. 254
  23. 33rd
  24. 6
  25. 336
  26. 90
  27. 276
  28. 35
  29. 176
  30. 34th
  31. 80
  32. 396
  33. 402
  34. 400
  35. 354
  36. 3655
  37. 3081
  38. 231
  39. 294
  40. 4371

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